Question

Can a triangle with sides 7, 10, and 12 be a right triangle? How do you know?(1 point)
Responses

No, because 149 does not equal 144.
No, because 149 does not equal 144.

There is no way to tell without an angle measure.
There is no way to tell without an angle measure.

No, because 193 does not equal 100.
No, because 193 does not equal 100.

Yes, because it looks like a right triangle.
Yes, because it looks like a right triangle.
Remaining Attempts : 3

Answer 1

To determine if a triangle with sides 7, 10, and 12 can be a right triangle, we can use the Pythagorean theorem. According to the theorem, a triangle is a right triangle if the sum of the squares of the two shorter sides equals the square of the longest side.

Let's identify the sides:
- The sides are 7, 10, and 12. The longest side is 12.

Now we can apply the Pythagorean theorem:

1. Calculate the square of the longest side (12):
\[
12^2 = 144
\]

2. Calculate the sum of the squares of the two shorter sides (7 and 10):
\[
7^2 + 10^2 = 49 + 100 = 149
\]

Now we compare the two results:
- \( 7^2 + 10^2 = 149 \)
- \( 12^2 = 144 \)

Since \( 149 \) does not equal \( 144 \), the triangle with sides 7, 10, and 12 cannot be a right triangle.

Therefore, the correct response is:
**No, because 149 does not equal 144.**